Ques 1.

Find floating point representation, if possible normalized, in the 4-digit mantissa, two digit
exponent, if necessary use approximation for each of the following numbers: (8)
(i) 27.94 (ii) -0.00943 (iii) -6781014 (iv) 0.0644321
Also, find absolute error, if any, in each ca

Ques 2.

Convert the decimal integer -465 to binary using both the methods (as shown in Pg No:16 of Block-1) . Show all the steps.

Ques 3.

Convert the number given as binary fraction –(0.101110101)2 to decima

Ques 4.

Find the sum of the two floating numbers x1=0.1364X101 and x2=0.7342X10-1. Further express the result in normal form, using (i) Chopping (ii) Rounding. Also, find the absolute error

Ques 5.

Solve the system of equations (5)
2 x + y + z = 3
 x + 3y + 3z = 4
 x – 4y + 2z = 9

Ques 6.

Perform four iterations (rounded to four decimal places) using 
(i) Jacobi Method and
(ii) Gauss-Seidel method ,
for the following system of equations.

Ques 7.

Determine the smallest positive root of the following equation: 
f(x) ≡ x3 – 9x2
- x + 9 = 0
to three significant digits using
(a) Regula-falsi method (b) Newton-Raphson method
(c) Bisectionmethod (d) Secant method

Ques 8.

Find Lagrange’s interpolating polynomial for the following data. Hence obtain the value of
f(4). (5)
x 0 2 3 5
f(x) 2 11 21 121

Ques 9.

Using the inverse Lagrange’s interpolation, find the value of x when y=3 for the following   data: 
x 25 35 55 75
y=f(x) -2 -1 1 5

Ques 10.

The population of a country for the last 25 years is given in the following table:. 
Year (x) : 1995 2000 2005 2010 2015
Population in lakhs (y) : 678 1205 1855 2745 3403

Ques 11.

(i) Using Stirling's central difference formula, estimate the populationfor the year 2007
(ii) Using Newton’s forward formula, estimate the population for theyear 1998.
(iii) Using Newton’s backward formula, estimate the population for theyear 2013.

Ques 12.

Derive the relationship for the operators δ in terms of E.

Ques 13.

Find the values of the first and second derivatives of y = f(x) for x=2.1 using the (5)
following table. Use forward difference method. Also, find Truncation Error (TE) and
actual errors.
x : 2 2.5 3 3.5
y : 8.7 12.7 16.8 20.9

Ques 14.

Find the values of the first and second derivatives of y = f(x) for x=2.1 from the (5)
following table using Lagrange’s interpolation formula. Compare the results with (a)
part above.
x : 2 2.5 3 3.5
y : 8.7 12.7 16.8 20.9

Ques 15.

Compute the value of the integral 
8
∫ 0 (4 x4+ 5x3 + 6x +5) dx
By taking 8 equal subintervals using (a) Trapezoidal Rule and then
(b) Simpson's 1/3 Rule. Compare the result with the actual value.